How to Convert Decimal Degrees to DMS
Geographic coordinates (latitude and longitude) can be written in two common formats: decimal degrees (DD), such as -41.28650, and degrees, minutes, seconds (DMS), such as 41 degrees 17 minutes 11.4 seconds South. Both describe exactly the same point on Earth. Converting between them uses simple base-60 (sexagesimal) arithmetic, the same system used for hours, minutes and seconds in time.
To convert decimal degrees to DMS:
- Take the whole number part of the decimal value. This is the degrees.
- Multiply the remaining decimal fraction by 60. The whole number part of this result is the minutes.
- Multiply the new remaining fraction by 60. The result is the seconds.
Example: convert -41.28650 (Wellington's latitude) to DMS.
| Step | Calculation | Result |
|---|
| Degrees | Whole number part of 41.28650 | 41 degrees |
| Minutes | 0.28650 x 60 | 17.19 → 17 minutes |
| Seconds | 0.19 x 60 | 11.4 seconds |
| Result | | 41 degrees 17' 11.4" S |
The negative sign on the decimal value indicates the Southern hemisphere (for latitude) or Western hemisphere (for longitude), so it is dropped and replaced with a hemisphere letter (N, S, E or W) in DMS format.
How to Convert DMS Back to Decimal Degrees
To reverse the process, divide the minutes by 60 and the seconds by 3600, then add both to the degrees:
Decimal degrees = Degrees + (Minutes / 60) + (Seconds / 3600)
Using the same example: 41 + (17 / 60) + (11.4 / 3600) = 41 + 0.28333 + 0.00317 = 41.28650. If the hemisphere is South or West, apply a negative sign to the final result.
Why the Formats Matter
Decimal degrees are the standard for digital mapping tools such as Google Maps, GPS devices, and GIS software, because they are easy to store as a single number and simple to calculate distances or areas with. Degrees, minutes, seconds format is the traditional navigation and surveying format, and it is still widely used on nautical charts, in aviation, and in New Zealand legal land descriptions and Land Information New Zealand (LINZ) survey records.
Common NZ Coordinate Examples
| Location | Decimal Degrees | DMS |
|---|
| Wellington | -41.28650, 174.77622 | 41 degrees 17' 11.4" S, 174 degrees 46' 34.4" E |
| Auckland | -36.84850, 174.76330 | 36 degrees 50' 54.6" S, 174 degrees 45' 47.9" E |
| Christchurch | -43.53210, 172.63620 | 43 degrees 31' 55.6" S, 172 degrees 38' 10.3" E |
Frequently Asked Questions
How do you convert decimal degrees to degrees, minutes and seconds?
Take the whole number part as degrees, multiply the remaining fraction by 60 for minutes, then multiply that remaining fraction by 60 again for seconds.
How do you convert DMS back to decimal degrees?
Use decimal degrees = degrees + (minutes / 60) + (seconds / 3600), applying a negative sign for South or West.
Why do GPS coordinates use different formats?
Decimal degrees suit digital mapping and calculations, while DMS is the traditional format still used in navigation, surveying and legal land descriptions in New Zealand.
Related Calculators
Sources: Land Information New Zealand (LINZ) geodetic coordinate conventions (linz.govt.nz). Standard sexagesimal (base-60) coordinate notation used in navigation and surveying worldwide.
This calculator uses standard mathematical conversion between decimal degrees and degrees, minutes, seconds formats. It does not account for different geodetic datums (such as NZGD2000 vs WGS84), which can shift coordinates by a small amount. For survey-grade or legal purposes, consult a licensed surveyor or LINZ data.
